forthcoming: FORMALIZATIONS OF RATIONAL CHOICE IN THE 20th CENTURY: FROM AXIOMS TO PREFERENCE CONDITIONS

Goran S. Milovanović

Abstract of the talk for the forthcoming 30th Annual Conference of the European Society for the History of Human Sciences, Belgrade, 5-8 July 2011.

The problem of choice under risk is inherently related to foundational problems of cognitive psychology via the notion of the measurement of belief. The second half of the 20th century witnessed a renewed interest in this problem, following Daniel Bernoulli’s early analysis of choice behavior (1738), von Neumann and Morgenstern’s (1947) axiomatization of rational choice under risk, and Ramsey (1926), de Finetti (1937) and Savage’s (1972) seminal work in the subjectivist foundations of probability theory. While the formal, theoretical foundations of choice under risk were laid in economics and mathematics, where they continue to receive critical reassessment and attention, the empirical phenomena of choice did not receive systematic experimental treatment until the cognitive revolution in psychology reaffirmed questions related to the measurement of belief in the second half of the century.

Theories of choice under risk present the domain best suited for exact methodological and theoretical analyses in cognitive psychology, owing this property to their well developed, axiomatic formal structure. Paradigmatically, the construction of a theory of choice under risk is based on a proof of the respective representation theorem. A representation theorem provides a basis for the measurement of belief by linking the theory’s axiomatic assumptions, which are directly related to observable choice behavior, with the existence of a utility (or value) function that maps the objects of choice to the set of real numbers. The theories of choice are then empirically tested against (a) the empirical violations of their axiomatic assumptions and (b) the capacity to encompass a body of empirical findings established in psychological research.

The most important line of this paradigmatic approach begins with Allais’ (1953, Jallais & Pradier, 2005) empirical critique of the normative theory of Expected Utility (EU, von Neumann & Morgenstern, 1947), and results in (i) the development of systematic experimental tests of the normative theory (Reed, 2009), and (ii) the development of new formal theories of choice under risk. In the scope of the later development, the theories of Rank-Dependent Utility (RDU, Schmidt, 2004, Abdellaoui, 2009), and specifically a special case of RDU known as Cumulative Prospect Theory (CPT, Kahneman & Tversky, 1979, Tversky & Kahneman, 1992, Wakker & Tversky, 1993, Chateauneuf & Wakker, 1999), are recognized as consistently the best, both mathematically sound and empirically valid, answer to the challenges posed by experimental studies.

We follow and discuss three important, interrelated developments that take place in the discourse of this research paradigm. The first is related to the progressive loss of intuitive grounds in the axiomatizations of choice under risk following the development of mathematical alternatives to EU. As axiomatic assumptions on choice behavior in these theories tend to become more complex, a recent textbook (Wakker, 2010) on CPT even drops the term “axioms” in favor of “preference conditions”. The second is the absence of successful convergent methodological operations in the experimental studies of choice under risk. Some of the “signature” findings, such as the famous Allais’ paradox, are not well-behaved under replication with even slight methodological variations (Reed, 2009). The question of how exactly such empirical phenomena motivated and influenced the developments in the second half of the 20th century is raised. Finally, the third development we present is the perception of obligation on the behalf of professionals in cognitive psychology to conform to the axiomatic approaches characteristic of the tradition in economics and mathematics.

We aim to suggest a conclusion of theoretical and methodological nature following our historical analysis: as early as in the 18th century, Daniel Bernoulli was able to present a formal analysis of choice that successfully accounted for some of the most important “signature phenomena” of choice relying solely on simple, elementary empirical intuition. In spite of the great progress in the formal analysis of choice under risk, it is suggested that a different, intuition-driven research paradigm would be more appropriate for psychological studies of choice under risk. It is also suggested that intuition-driven research paradigms need not abandon a priori any of the formal results developed thus far.

Selected Bibliography:

Abdellaoui, M. (2009). Rank-Dependent Utility. In Anand, Pattanaik & Puppe (eds) Rational and Social Choice: An Overview of New Foundations and Applications, New York: Oxford Univerisity Press.

Allais, M. (1953). Le comportement de l’homme rationnel devant le risque: critique des postulats et axiomes de l’école Américaine, Econometrica 21, 503-546.

Bernoulli, D. (1738).  Specimen Theoriae Novae de Mensura Sortis, Comentarii Academiae Scientiarum Imperialis Petroolitanae, Tomus V, 1738, pp. 175-192; Originally published in 1738; translated by Dr. Lousie Sommer, (1954). Exposition of a New Theory on the Measurement of Risk, Econometrica 22(1): 22–36.

Chateauneuf, A. &  Wakker, P. (1999). An Axiomatization of Cumulative Prospect Theory for Decision under Risk. Journal of Risk and Uncertainty 18, 137-145.

de Finetti, B. (1937/1964). La Prévision: ses lois logiques, ses sources subjectives. English translation: Foresight: its Logical Laws, Its Subjective Sources, in Kyburg & Smokler (eds), Studies in Subjective Probability. New York: Wiley, 1964.

Jallais, S. & Pradier, P. C. (2005). The Allais Paradox and its immediate consequences for expected utility theory. In Fontaine & Leonard (Eds), The Experiment in the History of Economics. New York: Routlage.

Kahneman, D. & Tversky, A. (1979). Prospect Theory. An Analysis of Decision under Risk. Econometrica, 47:2, 263-91.

Neumann, von J. & Morgenstern, O. (1947). Theory of Games and Economic Behavior (2nd revised edition). Princeton: Princeton University Press.

Reed, D. (2009). Experimental Tests of Rationality. In Anand, Pattanaik & Puppe (eds) Rational and Social Choice: An Overview of New Foundations and Applications, New York: Oxford Univerisity Press.

Savage, L. J. (1972). The Foundations of Statistics (2nd revised edition). New York: Dover Publications.

Schmidt, U. (2004). Alternatives to Expected Utility: Formal Theories. In Barbera & Seidl (eds), Handbook of Utility Theory: Vol. 2: Extensions, Boston: Kluwer Academic Publishers.

Tversky, A. & Kahneman, D. (1992). Advances in Prospect Theory: Cumulative Representation of Uncertainty. Journal of Risk and Uncertainty, 5(4), 297–323.

Wakker, P. (2010). Prospect Theory For Risk and Ambiguity. Cambridge: Cambridge University Press.

Wakker, P. & Tversky, A. (1993). An Axiomatization of Cumulative Prospect Theory. Journal of Risk and Uncertainty 7, 147-176.